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Presentation
Presentation
The Probabilities and Statistics course provides the fundamental principles of statistical analysis and probability theory, which are essential for the collection, organization, analysis, and interpretation of data under conditions of uncertainty. It covers descriptive statistics, probability theory, probability distributions, statistical inference, interval estimation, hypothesis testing, as well as correlation and linear regression techniques. The course focuses on quantitative data analysis and decision support in industrial, business, technological, and service organizations. It develops students' skills in modelling and interpreting random phenomena, analysing statistical evidence, and validating hypotheses, constituting a fundamental component of education in engineering, management, and applied sciences by promoting a rigorous, data-driven approach to solving real-world problems.
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Class from course
Class from course
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Degree | Semesters | ECTS
Degree | Semesters | ECTS
Bachelor | Semestral | 5
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Year | Nature | Language
Year | Nature | Language
2 | Mandatory | Português
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Code
Code
ULHT46-620
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Prerequisites and corequisites
Prerequisites and corequisites
Not applicable
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Professional Internship
Professional Internship
Não
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Syllabus
Syllabus
Descriptive statistics: main measures of central, non-central tendency and of dispersion. Linear correlation and regression. Random experience. Event. Sample space. Algebra of events. Probability concepts (Laplace and Kolmogorov). Conditional probability. Independence. Discrete and continuous random variables. Probability and distribution functions. Mathematical expectation: mean, variance, and standard deviation. Discrete distributions. Uniform, Bernoulli, Binomial and Poisson distributions. Continuous distributions. Normal, Chi-square, t-student, and exponential distribution. Statistical inference. Sampling distributions. Central limit theorem. Range estimation. Confidence interval for the mean, known and unknown variance, large and small sample. Interval for the proportion. Tests of Hypotheses for the mean and the proportion.
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Objectives
Objectives
Upon successful completion of this course, students will be able to master the fundamental tools of descriptive statistics and understand linear correlation and regression, including the interpretation of their results. They will be able to compute and interpret the main statistical measures and identify their properties. Students will acquire the ability to calculate probabilities using Laplace's definition and Kolmogorov's axiomatic framework, determine conditional probabilities, and apply the multiplication rule, the law of total probability, and Bayes' theorem. They will understand the concept of random variables and work with probability functions and probability distributions. Furthermore, students will become familiar with the most important discrete and continuous probability distributions and their main properties. They will also be able to construct and interpret confidence intervals, perform hypothesis tests, and draw statistically sound conclusions from the results obtained.
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Teaching methodologies
Teaching methodologies
Exercise sets will be assigned throughout the course to consolidate students' knowledge and strengthen their problem-solving skills. In each session, students are encouraged to work independently on problems related to the topics covered in class and to present their solutions in the following session. Particular emphasis is placed on the idea that solving exercises is not an end in itself, but rather a means of developing a deeper understanding of the theoretical concepts covered in the course. Mastery of these concepts enables students to apply statistical methods effectively to more complex and practical problems. The course follows a progressive learning approach, beginning with descriptive statistical methods and advancing towards the more conceptual topics of probability theory and statistical inference. This progression is designed to consolidate students' understanding of the various statistical tools and to develop their ability to apply them.
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References
References
Murteira, B., Ribeiro, C. S., Andrade e Silva, J., & Pimenta, C. (2023). Introdução à Estatística (4.ª ed.). Escolar Editora. Murteira, B., & Antunes, M. (2013). Probabilidades e Estatística (Vols. I e II). Escolar Editora. Niewiadomska-Bugaj, M., & Bartoszy¿ski, R. (2021). Probability and Statistical Inference (3rd ed.). John Wiley & Sons. Pedrosa, A. C., & Gama, S. M. (2018). Introdução Computacional à Probabilidade e Estatística . Porto Editora.
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Assessment
Assessment
Descrição dos instrumentos de avaliação (individuais e de grupo) ¿ testes, trabalhos práticos, relatórios, projetos... respetivas datas de entrega/apresentação... e ponderação na nota final.
Exemplo:
Descrição
Ponderação
Teste 1
40%
Teste 2 50%
TPC/Participação 10%
Frequência global 90% + 10% Exame 100%
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Mobility
Mobility
No
